Simulation of coalescence, break up and mass transfer in bubble columns by using the Conditional Quadrature Method of Moments in OpenFOAM

The evaluation of the mass transfer rates and the fluid-dynamics aspects of bubble columns are strongly affected by the intrinsic poly-dispersity of the gas phase, namely the different dispersed bubbles are usually distributed over a certain range of size and chemical composition values. In our previous work, gas-liquid systems were investigated by coupling Computational Fluid Dynamics with mono-variate population balance models (PBM) solved by using the quadrature method of moments (QMOM). Since mass transfer rates depend not only on bubble size, but also on bubble composition, the problem was subsequently extended to the solution of multi-variate PBM (Buffo et al. 2013). In this work, the conditional quadrature method of moments (CQMOM) is implemented in the open-source code OpenFOAM for describing bubble coalescence, breakage and mass transfer of a realistic partially aerated rectangular bubble column, experimentally investigated by Diaz et al.(2008). Eventually, the obtained results are here compared with the experimental data availabl

Modelling the Interfacial Flow of Two Immiscible Liquids in Mixing Processes

This paper presents an interface tracking method for modelling the flow of immiscible metallic liquids in mixing processes. The methodology can provide an insight into mixing processes for studying the fundamental morphology development mechanisms for immiscible interfaces. The volume-of-fluid (VOF) method is adopted in the present study, following a review of various modelling approaches for immiscible fluid systems. The VOF method employed here utilises the piecewise linear for interface construction scheme as well as the continuum surface force algorithm for surface force modelling. A model coupling numerical and experimental data is established. The main flow features in the mixing process are investigated. It is observed that the mixing of immiscible metallic liquids is strongly influenced by the viscosity of the system, shear forces and turbulence. The numerical results show good qualitative agreement with experimental results, and are useful for optimisating the design of mixing casting processes

Population balance modelling of polydispersed particles in reactive flows

Polydispersed particles in reactive flows is a wide subject area encompassing a range of dispersed flows with particles, droplets or bubbles that are created, transported and possibly interact within a reactive flow environment - typical examples include soot formation, aerosols, precipitation and spray combustion. One way to treat such problems is to employ as a starting point the Newtonian equations of motion written in a Lagrangian framework for each individual particle and either solve them directly or derive probabilistic equations for the particle positions (in the case of turbulent flow). Another way is inherently statistical and begins by postulating a distribution of particles over the distributed properties, as well as space and time, the transport equation for this distribution being the core of this approach. This transport equation, usually referred to as population balance equation (PBE) or general dynamic equation (GDE), was initially developed and investigated mainly in the context of spatially homogeneous systems. In the recent years, a growth of research activity has seen this approach being applied to a variety of flow problems such as sooting flames and turbulent precipitation, but significant issues regarding its appropriate coupling with CFD pertain, especially in the case of turbulent flow. The objective of this review is to examine this body of research from a unified perspective, the potential and limits of the PBE approach to flow problems, its links with Lagrangian and multi-fluid approaches and the numerical methods employed for its solution. Particular emphasis is given to turbulent flows, where the extension of the PBE approach is met with challenging issues. Finally, applications including reactive precipitation, soot formation, nanoparticle synthesis, sprays, bubbles and coal burning are being reviewed from the PBE perspective. It is shown that population balance methods have been applied to these fields in varying degrees of detail, and future prospects are discussed

ON THE IMPLEMENTATION OF MOMENT TRANSPORT EQUATIONS IN OPENFOAM TO PRESERVE CONSERVATION, BOUNDEDNESS AND REALIZABILITY

Different industrial scale multiphase systems can be successfully described by considering their polydispersity (e.g. particle/droplet/bubble size and velocity distributions) and phase coupling issues are properly overcome only by considering the evolution in space and time of such distributions, dictated by the so-called Generalized Population Balance Equation (GPBE). A computationally efficient approach for solving the GPBE is represented by the quadrature-based moment methods, where the evolution of the entire particle/droplet/bubble population is recovered by tracking some specific moments of the distribution and the quadrature approximation is used to solve the "closure problem" typical of moment-based methods. In this contribution some crucial computational and numerical details concerning the implementation of these methods into the opensource Computational Fluid Dynamics (CFD) code OpenFOAM are discussed. These aspects are in fact very often overlooked, resulting in implementations that do not satisfy the properties of conservation, realizability and boundedness. These constraints have to be satisfied in a consistent way, with respect to what done with the other conserved transported variables (e.g. volume fraction of the disperse phase) also when higher-order discretization schemes are used. These issues are illustrated on examples taken on our work on the simulation of fluid-fluid multiphase system

Computational Fluid Dynamics Analysis of Two-Phase Chemical and Biochemical Reactors

In this work, the numerical analysis of turbulent two-phase processes in stirred tanks and bioreactors is performed with a computational fluid dynamics (CFD) approach. The modelling of the turbulent two-phase phenomena is achieved in the context of the Reynolds Averaged Navier-Stokes (RANS) equations and the Two-Fluid Model (TFM). Different modelling strategies are studied, tested and developed to improve the prediction of mixing phenomena, interphase interactions and bio-chemical reactions in chemical and process equipment. The systems studied in this work are a dilute immiscible liquid-liquid dispersion and dense solid-liquid suspensions, both in stirred tanks of standard geometry, a gas-liquid system consisting of a dual impeller vortex ingesting fermenter for the production of biohydrogen, analyzed in two different configurations of the supports for the attached growth of biomass, and two different bioreactors, of different scale and configuration, subject to substrate concentration segregation. Purposely collected experimental data and data from the literature were extensively used to validate the numerical results and either confirmed the goodness of the models and the modelling techniques, helped the definition of the limits and the uncertainties of the model formulations or guided the development of new models. In all cases, particular attention was devoted to the precision of the numerical solution, and to the validation with experimental data to quantify the appropriateness of the models and the accuracy of the CFD predictions

Predicting adaptive responses - simulating occupied environments

Simulation of building performance is increasingly being used in design practice to predict comfort of occupants in finished buildings. This is an area of great uncertainty: what actions does a person take when too warm or suffering from glare; how is comfort measured; how do groups of people interact to control environmental conditions, etc? An increasing attention to model these issues is evident in current research. Two issues are covered in this paper: how comfort can be assessed and what actions occupants are likely to make to achieve and maintain a comfortable status. The former issue describes the implementation of existing codes within a computational framework. This is non-trivial as information on local air velocities, radiant temperature and air temperature and relative humidity have to be predicted as they evolve over time in response to changing environmental conditions. This paper also presents a nascent algorithm for modelling occupant behaviour with respect to operable windows. The algorithm is based on results of several field studies which show the influence of internal and external temperatures on decision making in this respect. The derivation and implementation of the algorithm is discussed, highlighting areas where further effort could be of benefit

Population balance modelling of soot formation in laminar and turbulent flames

The reduction of soot emissions in combustion processes is a primary concern of combustion engineers due to the severe health impact of soot, and the prediction of the soot particle size distribution (PSD) has become important. The evolution of the PSD can be predicted by solving the population balance equation (PBE), and several approaches have been proposed for introducing soot morphology in the PBE. Furthermore, the PBE must be coupled with fluid dynamics, species transport and chemical kinetics in order to predict soot properties in laminar and turbulent flames. Finally, accurate and computationally efficient methods must be employed for solving the CFD-PBE approach. In the first part of this thesis, the recently developed conservative finite volume sectional method for the solution of the population balance equation (PBE) is extended to a two-PBE approach for modelling soot formation that distinguishes between coalescence and aggregation and accounts for finite-rate fusing of primary particles within aggregates, while providing a numerically accurate description of primary particle surface growth and oxidation within aggregates. The validation of the method is conducted by reproducing the self-preserving distributions of aggregates with varying fractal dimension. Subsequently, the one-PBE and two-PBE approaches are coupled with CFD and applied to the application of the Santoro laminar non-premixed co-flow sooting flame. By using a comprehensive soot kinetic model, the deficiencies of the one-PBE approach are analysed, and the two-PBE approach is shown to provide a significant improvement in the description of soot morphology using a properly adjusted particle fusing rate. At present, the model parameters for the fusing of soot primary particles are based on sintering models from silica and titania nanoparticles due to the lack of experimental data for soot. Therefore, a comprehensive sensitivity analysis of the model parameters is conducted. The results show the predictive potential of both the one-PBE and two-PBE approaches. With the presently available experimental measurements, the results suggest that one-PBE method is a reasonable choice for the applications associated with turbulent flame. Subsequently in the second part, the one-PBE method is incorporated into the LES-PBE-PDF approach developed within the group for modelling soot formation in turbulent flames. For the first time, the LES-PBE-PDF approach provides a comprehensive physicochemical model accounting for nucleation, surface growth, oxidation, condensation, coalescence and aggregation. The interaction between chemistry, turbulence and soot particles are accounted for by resolving an evolution equation for the LES-filtered one-point, one-time, joint scalar-number density probability density function (PDF). The Eulerian stochastic field method is used for the solution of the joint-scalar-number density PDF. By using the same kinetics and model parameters as tested in the laminar flame case, the LES-PBE-PDF approach is applied to model soot formation in the Sandia turbulent non-premixed sooting flame. The predicted thermochemical conditions and soot volume fraction are in reasonably good agreement with experimental measurements. The analysis and findings demonstrate good predictive capability and computational feasibility of the complete LES-PBE-PDF approach. In summary, this thesis presents a systematic study for soot formation in the laminar and turbulent flames. In particular, the key adjustable model parameters, surface reactivity $\alpha$ and cut-off point $d_c$, are calibrated in the laminar flame and employed in the turbulent flame. Yet, some limitations should be pointed out. For soot study, the current methodology does not capture the composition of soot during its formation and growth, thus the surface reactivity model applied is rather primitive and needs some adjustments, and the work assumes a constant fractal dimension, whose impact should be further investigated. For turbulent sooting flame, future investigation regarding the micromixing model is warranted.Open Acces